This invention relates to thermoresistive sensor systems and specifically to those sensor systems that compensate for changes in ambient temperature. In the preferred application, this invention relates to measuring a liquid level with a thermoresistive sensor system which compensates for changes in temperature of a medium.
It is well known in the art to use thermoresistive sensors for monitoring parameters such as flow or level of a medium. For example, a resistive sensor may be heated and the resistance of the sensor may be measured to determine changes in heat transfer conditions around the sensor. This change is used to determine the flow or level of a medium. In such systems, changes in the temperature of the medium will cause the sensor resistance to increase or decrease, thus, affecting the measurement and potentially causing an error.
One solution to this potential error is to maintain constant power on a first of two sensors that are mounted side-by-side in the medium. A current is supplied to the second sensor which is at a ratio of the current through the first sensor. The voltages across the first and second sensors are processed to an output. This output is representative of the changes in the medium, such as a change in the level of a liquid in the medium or a change in the flow of the medium. This constant power source system partially compensates for changes in the medium temperature, and works well where temperature variation in the medium is small.
The following mathematics show the partial compensation of a constant power system. Assuming no self heating of the first sensor, the resistances of the first and second sensors are approximated by: EQU R.sub.1 =R.sub.0 (1+.alpha..DELTA.T.sub.a) (1) EQU R.sub.2 =R.sub.0 (1+.alpha..DELTA.T.sub.a +.alpha..DELTA.T.sub.q) (2)
where
R.sub.0 is the resistance of the censors at 0.degree. C., PA1 .alpha.is the temperature co-efficient of resistance of the sensor material, PA1 .DELTA.T.sub.a is the difference between T.sub.0, which is 0.degree. C., and the temperature of the medium, and PA1 .DELTA.T.sub.q is the difference between T.sub.a and the temperature of the second probe. PA1 q" is the surface heat flux and PA1 h is the thermal heat transfer coefficient of the sensor. In terms of power supply to the sensor ##EQU1## where I is the current through the sensor and A is the surface area of the sensor. By combining equations 3 and 4 .DELTA.T.sub.q is given by equation ##EQU2##
For a sensor that is self-heated, that is heated by applying a current through it, the surface heat flux of that sensor is given by: EQU q"=h.DELTA.T.sub.q (3)
where
In order to determine the .DELTA.T.sub.q of the sensor without knowing its resistance due to the self heating of the sensor, R of equation 5 is replaced with equation 2 whereby .DELTA.T.sub.q is then given by ##EQU3##
The resistance of a sensor in terms of its thermal resistive properties can now be determined by substituting equation 6 into equation 2 which gives ##EQU4## equation 7 can be simplified by using the approximation ##EQU5## which is true when X is small. Then the resistance of the sensor which is self-heated is given by ##EQU6##
A self-heating current I.sub.2 is passed through the second sensor and the first sensor receives a current I.sub.1 which is a fraction of the second sensor's current I.sub.2. This current I.sub.1 is insufficient to cause significant self-heating of the first sensor. Thus, self-heating in the first sensor may be ignored for present purposes. The voltage across the first sensor V.sub.1 is then amplified by the ratio of the two currents I.sub.1 and I.sub.2. The voltages across the two sensors can be developed from equation number 9. The difference between these two voltages is represented by ##EQU7##
This is approximately what the difference in sensor voltages will be.
Now because constant power is maintained in the first sensor, it follows that: EQU I.sub.0.sup.2 R.sub.0 =I.sub.1.sup.2 R.sub.1 (11)
Thus, EQU I.sub.1 =I.sub.0 (1+.alpha..DELTA.T.sub.a).sup.-1/2 (12)
and substituting equation 12 into equation 10, .DELTA.V is equal to ##EQU8##
Equation 13 indicates that constant power to compensate for temperature drift of the medium is not a full compensation, since .DELTA.V is dependent to some extend upon .DELTA.T.sub.a which is the difference between the medium temperature and initial temperature.
More precise temperature compensation may be needed in some applications and it is provided by the present invention.